You could check the voltage at the battery terminal when cranking the starter ... if it drops to 6v like the starter input then it's the battery but if it stays up around 12v it's likely a bad connection issue in one of the heavy cables to the starter
K
Sorry I disagree with that second statement K, if I've understood correctly. Note also the OP has already stated the voltage measured at starter motor whilst it's operating is 6 volts.
If however the voltage measured under same circumstances is in the order of 11 to 12 volts everything would be normal. It certainly wouldn't indicate a faulty battery cable connection.
The measured 6 volts at starter could be down to battery itself temporarily not being able to maintain a higher voltage due to the attempted current draw from its limited capacity. It could also be caused by severe volt drop at the point of a poor battery cable connection though with attendant local heat, and with similar results regarding starter operation.
As mentioned above I favour the battery being at fault almost irrespective of it's age, particularly as OP mentioned dash voltmeter dropping to 5 volts (likely a little pessimistic) whilst starter operating. This suggesting minimal voltage drop on battery cable run.
